So first of all I am not a multiplayer expert. The following remarks are based off of following the game just recently.

I understand some people seem to think the Knalgan Alliance is underpowered in competitive MP. The claim, as it goes, is that 4 movement points for the Knalgan mainstay units is just too few, and an insurmountable hindrance against opponents who know how to exploit this lack of mobility. The result is experienced players with Knalga in MP seem to spam footpads and thieves.

I personally really don't know enough about MP balance to weigh in on the discussion, however I have made an observation that if acted upon may please everyone who likes this game.

Thematically, Dwarves are my favorite faction, and I have recently noticed something rather unfortunate about them in MP. Namely, not a single one of their units has multiple promotion paths. Compared to the other factions this is surprising. Even the Northerners have some branching, not to mention the other four (Spearman with three choices).

I don't think multiple promotion paths is ever a bad thing, especially since it effects balance so indirectly, and is not actually adding another unit to the recruitment pool as has been suggested in the past (Dwarven Scout from campaigns).

One strength of Dwarven units is that they are tough. Furthermore, they are PREDICTABLY tough. Their defenses are on average low, but their resistances high, which along with high hitpoints makes keeping individual units alive somewhat easier than with other factions. This means that if I knew that I could promote my Dwarven Fighter to some variant with better mobility than a Steelclad, I could probably ensure that happens.

And that is essentially my entire suggestion, that at least two Dwarven units of the Knalgan Alliance be given multiple promotion paths. Let the Dwarves have some love!

Knalgan isn't so much a problem compared to Loyalist slight overpoweredness
Dwarves are good units, and are OP in some maps (especially smaller ones)
Current Dwarven promotion is superior than mobility based promotions and are some of the best level 2s in game.
Having new promotions in default will affect campaigns more than multiplayer
You can use add-ons that use other dwarven units not found in default.

Regarding Dwarven promotion being good, sure, it certainly is, for the most part. Actually the Dwarven Fighter might have one of the best promotions for XP in game. The Gryphon Master is up there too. I wouldn't, however, call the Dwarvish Thunderguard one of the best level 2's in game. It's an improvement of only 10 HP, which admittedly has to be multiplied by resistances, and not particularly much damage. I understand the utility of a 28 damage attack, even if there are other ranged level 2's that potentially deal more. It's far more likely to instantly deal 28 damage, as opposed to having every one of four seven damage attacks hit. This forces your opponent to adopt a somewhat reactionary playstyle, and in general the Thunderguard is a powerful unit. I would not call it one of the best level 2's in game as it specifically doesn't one shot most units, which would make all the difference, and would be obviously overpowered.
The Dwarven Stalwart on the other hand feels like a downright pitiful promotion. 12 HP, 3 damage on ranged and 6 on melee, with an extra 10% defensiveness on flat, forest, and sand terrain, of which in particular flat is very common. Crucially, no improvement to defensiveness in villages. I understand that 12 HP goes a long way when you have 40% resists because of steadfast, but the 6 damage increase is laughable. The promotion also requires 47 XP, a totally unjustifiable amount, especially for such a low damage unit which is not likely to be getting death blows. If the Stalwart had a 10% defensiveness increase in villages, that would be something, because opponents are frequently forced to attack villages. But as it stands, the Dwarven Stalwart can essentially be ignored by the enemy, watching helplessly as units who should have gotten the XP to promote die around him.

I cannot comment regarding the overpoweredness of Loyalists.

Of course Dwarven units are OP on certain maps, as is the case for practically all factions on practically all maps. Winrates are always going to depend on the given map.

I mean I have absolutely no idea how much thought was put into balancing promotion paths, however I imagine a lot, and I know it generally is not something people rely on heavily as part of a strategy.
That being said, I do wonder to what extent the Spearman having three promotion possibilities is just a relic of someone liking the Loyalist faction. It's like, you need a tough pierce resistant unit pierce damage dealing unit? Pikeman. Hardy against blade? Swordsman. Ranged deterrent? Javelineer. You get my point, and perhaps you agree, since you consider Loyalists to be overpowered anyway.

Sure new promotions will affect campaigns, and this is why campaigns need to be maintained, not improvements to the game neglected.
I think your comment on mobility based promotions betrays a certain rigidity of thinking, as everything depends on the numbers. If Dwarven Fighter had a promotion to Dwarven Avenger (Justified in lore, etc. etc.) or something, a unit with 5 movement points, 50 HP, 10x3 blade melee damage and a 7x2 blade ranged attack, along with perhaps a 10% defensiveness boost in flat and forest terrain, but no resistances changes, would that not be worth considering (Really not sure how feasible exactly this unit seems, just trying to illustrate a point)?

The bottom line is that I do not see any balance reason for other factions having loads of promotion paths while the Knalgan Alliance has literally none. Even if the current Dwarven promotions were perfectly balanced, this still would not preclude the game being improved by adding more of them. Obviously "add-ons" is always an answer to every point that can be raised, but I see no downside to improving the mainline MP Knalgan Alliance.

P.S. Regarding Knalgan balance in general, as mentioned previously I actually do not think it is ideal, as evidenced by the Dwarvish Stalwart. Give that unit a 10% defensiveness boost in villages, or lower the XP requirement, or increase the damage, or whatever, but currently that unit is not viable, and I understood that at least on some level every unit should be viable. Personally I recommend a 10% defensiveness increase in villages, as that is the only way of justifying the XP cost while maintaining the specialization of the unit.
Aside from this I am an advocate of removing the resilient trait from Dwarven units. Lore wise, the assumption is that all Dwarven units are resilient, some of them are simply so tough, that they actually partially recover from their wounds immediately after battle (healthy). Far more importantly, of course, healthy is simply a better trait than resilient in essentially all circumstances, as it is only 3 less HP, which is really 1 less because it is incredibly rare to see a Dwarven unit die in one turn, even in MP. Every turn after that and the trait is better. The only unit this does not apply to is the Ulfserker. Other than that, removing resilient from the pool will allow Dwarven units to far more frequently get more important traits, such as intelligent, quick, and strong (well really all the other traits are more important, aren't they?).

The Knalgans technically have one promotion path: a Poacher becomes a Trapper, and a Trapper becomes either a Huntsman or Ranger. However, in standard 1v1 play the likelihood of seeing a level 3 unit seems fairly unlikely.

I have to admit, I'm not sure what promotion paths I'd add to the Knalgans. Maybe a Leadership alternative to the Steelclad? An alternative to the Outlaw that gets a Slow ranged attack (bola) but doesn't advance past level 2?

Oh, I did not know Poacher->Trapper has promotion branching. That's neat.

I think slow is an interesting idea. Since Dwarves are slow, and wear their enemies down in fights of attrition over multiple turns, it would make sense for them to want to slow enemies down so they could maintain pursuit.

Leadership is kind of boring in my opinion, and seems to already by quite prevalent among the other factions, plus I think it would be kinda difficult to balance 23 damage Thunderers (since as far as I know damage is rounded). I was thinking along similar lines, however, in terms of an ability that benefits other units. This is what I came up with:

Many guardsmen come to discover the power of a shield utilized offensively, and ultimately part with their spears completely. Their tower shield is made two handed, and the boss reinforced. Deceptively enough for their foes, their mighty shield thrusts are still highly dangerous at close quarters. Such troops are much beloved by their brothers in arms as their improved shields are easily large enough to accommodate more than one, and the Shieldbearers frequently go out of their way to protect their companions.

Special Notes: The size of this unit's shield as well as it's training increases the defense of nearby owned units to a point.

Attacks

shield impact 9x2 melee

Resistances

arcane 20%
blade 30%
cold 20%
fire 20%
impact 30%
pierce 30%

Terrain Modifiers
(same)

shieldwall

This unit increases adjacent owned unit's defenses by 10%, up to a maximum of 70%.

Obviously the numbers are all debatable, but the rationale for an alternate promotion path for the Guardsman is a unit that is still highly tanky by nature, but which the opponent also has reason to prioritize. The 70% cap is because I understand that BfW devs don't like the idea of higher defense than that, and I basically agree, it would not be fun attacking a dwarf in a mountain with 80% chance to miss. The resistance 10% increase across the board rationale is that this is a level 2 unit with the damage of an Orcish Grunt, but a massive shield which it is essentially impossible to bypass. This is also better than giving it the 10% defense increase in flat that Stalwarts have, as that would be too powerful, plus it creates an interesting situation where it shields all other units in this way but not itself (woe be unto those that face two Shieldbearers side by side). It loses the steadfast trait because even while attacking the shield will be held in the same defensive posture, but more importantly because in terms of gameplay this unit is not meant to be as hard to kill as the Stalwart.

I believe that these numbers are representative of the intention, and the idea of introducing a unit for the Knalgan Alliance that aids other units without having a straight up heal is cool. Tactically, it is also I believe an interesting ability which follows the much revered KISS principle. Heal doesn't do much if a unit is being specifically focused, as it will only ever restore 4/8 HP, and on the next turn, whereas this is always in effect.

P.S. Why are all the units Dwarvish this, Dwarvish that? Isn't it grammatically correct for it to be Dwarven? It would sound better too, imo.

I can think of other interesting and appropriate promotion paths, which I will not write out in such detail. I like your idea of a slowing human unit.
Perhaps the Shieldbearer need not advance to some level three unit, instead maybe the Guardsman has another option, still called Dwarven Phalangite, basically a unit without steadfast, but good pierce damage and first strike (although this might be far too similar to the Pikeman). I do like the idea of a level three Dwarven Shieldbearer though, it would be one of those units that are incredibly tough to level up, but unique and super tough.
Another option as initially mentioned is a Fighter variant which is basically balanced between ranged and melee, with an extra movement point, like the Scout/Pathfinder in campaigns.
Awesome would be a Dwarven Pistolier, a unit with an extra movement point, promoted from the Thunderer, but with two ranged attacks to account for two pistols, and the ability to move after attacking (with limitation, inevitably, so it is not overpowered, in fact probably literally one move back would be strong enough in terms of getting back into formation).
I can't really think of an interesting promotion path for the Ulfserker, that unit is pretty perfect as is already. Ranged berserk would be overpowered by default, can't really see that working, too many units with no ranged attack whatsoever.